Question

derive the expression for the frequency and time period of a body executing oscillations in case of a stretched string​

Answer 1

Explanation:

Time period T = time required to complete one oscillation.At equilibrium T0 = mg .For small displacement theta Restoring force = - mgsintheta for small

Answer 2

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$At \: equilibrium  \: T0=mg$

$For \: small \: displacement θ$

$Restoring \: force =−mg \: sinθ$

$for \: small θ \:  sinθ≈θ$

$⇒fe=−mgθ=−mg(lx)$

$acceleration a=mfe=l−g.x$

$We \: know \: for SHM, a \\ =−w {}^{2} x$

$⇒  On \: comparing \: we \: get w=lg$

$∴  Time \: period \: of \: oscillation  \: T \: \\ =w {}^{2} Π=2Πgl.$